Question
$$5+4 \cdot \frac{i}{3}i = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5+4 \cdot \frac{i}{3}i &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]3\cdot5+34 \cdot \frac{i}{3}i &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]15+4i^2 &= 0&& \text{simplify left side} \\[1 em]15-4 &= 0&& \text{simplify left side} \\[1 em]11 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 11 = 0 } $ is FALSE, we conclude that the equation has no solution.
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